May Catholics Married Outside the Church Go to Confession?

I infer you mean a Catholic who didn’t marry in a Catholic church, but who also didn’t have a dispensation from the Church to do so (See the Code of Canon Law, can. 1108, 1118, 1127). If that’s the case, then this Catholic has not married according to the laws of the Church and thus is not validly married in the eyes of God (see Matt. 16:18-19, 18:18). Such a person could go to confession, but to receive absolution from their sins, he would have to firmly resolve not to sin further (CCC 1451, 1490), which in his case would mean living as brother and sister with his spouse until their marriage was blessed/validated in the Church (see St. Pope John Paul II, Familiaris Consortio, 84).

If either spouse had been married previously, that would be a further complicating factor in any attempt to have their current marriage validated.